Question

Using $a^2-b^2=\left(a+b\right)\left(a-b\right),$ find
1) ${51}^2-{49}^2$
2) ${\left(1.02\right)}^2-{\left(0.98\right)}^2$
3) ${153}^2-{147}^2$
4) ${12.1}^2-{7.9}^2$

Answer 1

$a^2-b^2=(a+b)(a-b)$ -Identity

$1)$ ${51}^2-{49}^2=(51+49)(51-49)$

$=\left(100\right)\times \left(2\right)$

$=200$

$2)$ $(1.02{)}^2-(0.98{)}^2=(1.02+0.98)(1.02-0.98)$

$=\left(2\right)\times \left(0.04\right)$

$=0.08$

$3)$ $(153{)}^2-(147{)}^2=(153+147)(153-147)$

$=\left(300\right)\times \left(6\right)$

$=1800$

$4)$ $(12.1{)}^2-(7.9{)}^2=(12.1+7.9)(12.1-7.9)$

$=\left(20\right)\times \left(4.2\right)$

$=84$.